A common step in SBI is to reduce the dimensionality of the observed data before approximating the posterior distribution. This is particularly relevant when working with time series data, for which descriptions based on a few meaningful parameters is standard practice. For instance, the autocorrelation function is a sufficient statistic for signals generated by Gaussian autoregressive–moving-average (ARMA) models and is, therefore, the ideal summary feature extractor. For signals generated by complex non-linear simulators, such as the Hodgkin-Huxley or Lotka-Volterra models, the summary features are usually chosen based on previous domain knowledge [1]}. In this work, we propose a data-driven strategy that avoids tailoring summary statistics for each application.
